Breaking the lithosphere in extension without exceeding the driving far-field forces available on Earth is a tough quantitative modeling problem. One can tear it apart by propagation of an existing oceanic basin or weakness zone or one must assist rifting with magmatic processes, which drop the effective stress and weakens locally the lithosphere. While previous 3D models have demonstrated that non-cylindrical plumes produce almost cylindrical rift structures in a lithosphere under slight far-field loading, our contribution goes one step further by producing models of complete continental break-up. We investigate in details how the rheological stratification of the continental lithosphere interacting with active mantle plume influences the geometry and dynamics of rifting to continental break-up in 3D. We find that, irrespective of the rheological stratification, a plume-induced rifting process always occurs in two stages: an early crustal rifting stage and a late lithospheric necking (breakup) stage. In case of a rheologically decoupled lithosphere, initial brittle deformation is concentrated in the upper crust and strongly localized due to compensating ductile flow of lower-crustal material (core complex extension mode). On the contrary, rheological coupling between upper crust and lithospheric mantle results in highly distributed brittle deformation in the crust above mantle plume head (wide rift mode). Both core complex-like and wide rifting are followed by an abrupt transition to narrow rift stage when a localized ascent of mantle plume material focuses high strain along faults zones breaking through the entire lithosphere. The Main Ethiopian Rift, the Basin and Range province, and the East Shetland Basin may be natural examples of regions that have passed through these two stages of extension. Across-strike and along-strike asymmetry of break-up patterns arising spontaneously within initially symmetrical and laterally homogenous environment seems to be an intrinsic characteristic of plume-induced rifting.